---{"category_name":"medium","problem_code":"ADAFUN","problem_name":"Ada Function","languages_supported":{"0":"C","1":"CPP14","2":"JAVA","3":"PYTH","4":"PYTH 3.6","5":"PYPY","6":"CS2","7":"PAS fpc","8":"PAS gpc","9":"RUBY","10":"PHP","11":"GO","12":"NODEJS","13":"HASK","14":"rust","15":"SCALA","16":"swift","17":"D","18":"PERL","19":"FORT","20":"WSPC","21":"ADA","22":"CAML","23":"ICK","24":"BF","25":"ASM","26":"CLPS","27":"PRLG","28":"ICON","29":"SCM qobi","30":"PIKE","31":"ST","32":"NICE","33":"LUA","34":"BASH","35":"NEM","36":"LISP sbcl","37":"LISP clisp","38":"SCM guile","39":"JS","40":"ERL","41":"TCL","42":"kotlin","43":"PERL6","44":"TEXT","45":"SCM chicken","46":"PYP3","47":"CLOJ","48":"COB","49":"FS"},"max_timelimit":3,"source_sizelimit":50000,"problem_author":"alei","problem_tester":null,"date_added":"17-10-2018","tags":{"0":"alei","1":"dfs","2":"dynamic","3":"hard","4":"tries"},"editorial_url":"https://discuss.codechef.com/problems/ADAFUN","time":{"view_start_date":1548009002,"submit_start_date":1548009002,"visible_start_date":1548009002,"end_date":1735669800},"is_direct_submittable":false,"layout":"problem"}---<span class="solution-visible-txt">All submissions for this problem are available.</span>###Read problems statements in [Hindi](http://www.codechef.com/download/translated/COOK102/hindi/ADAFUN.pdf), [Mandarin Chinese](http://www.codechef.com/download/translated/COOK102/mandarin/ADAFUN.pdf), [Russian](http://www.codechef.com/download/translated/COOK102/russian/ADAFUN.pdf), [Vietnamese](http://www.codechef.com/download/translated/COOK102/vietnamese/ADAFUN.pdf) and [Bengali](http://www.codechef.com/download/translated/COOK102/bengali/ADAFUN.pdf) as well.Ada has a set of $N$ non-negative integers $S = \{x_1, x_2, \ldots, x_N\}$. She defined the function $W$ as follows:- $W(\{\}) = 0$.- If $S = \{a\}$, then $W(S) = a$.- If $S = \{a, b\}$ (so $|S| = 2$), then $W(S) = (a \oplus b) - 1$.- If $|S| \ge 3$, then to calculate $W(S)$, find any two elements of $S$ that are congruent (have the same remainders) modulo the highest possible power of $2$ (the highest power for which such a pair exists). Let's denote them by $a$ and $b$. Then $W(S) = W(\{a, b\}) \oplus W(S \setminus \{a, b\})$.- It is guaranteed that $W(S)$ is well-defined, i.e. does not depend on the exact choice of the two congruent elements.Here, $\oplus$ represents the binary XOR operation and $A \setminus B$ represents set difference.Ada needs to calculate the function $W$ for each set that is created by removing exactly one element from $S$. Formally, she wants to find $W(S \setminus \{x_i\})$ for each valid $i$. Can you help her?### Input- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.- The first line of each test case contains a single integer $N$.- The next line contains $N$ space-separated integers $x_1, x_2, \ldots, x_N$.### OutputFor each test case, print a single line containing $N$ space-separated integers. For each valid $i$, the $i$-th of these integers should denote $W(S \setminus \{x_i\})$.### Constraints- $1 \le T \le 10^6$- $1 \le N \le 10^5$- $0 \le x_i \le 10^{18}$ for each valid $i$- $x_1, x_2, \ldots, x_N$ are pairwise distinct- the sum of $N$ over all test cases does not exceed $10^6$### Example Input```160 1 2 5 7 8```### Example Output```13 4 3 0 6 5```